Finding Slope from a Table Notes interactive worksheet | Live ... - Free Printable

Let’s solve each table step by step to find the slope (m) using the formula:

> m = Δy / Δx = (y₂ - y₁) / (x₂ - x₁)

We’ll pick two points from each table — usually the first and second row, unless it’s easier otherwise. Since all tables show linear relationships, any two points will give the same slope.

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🔹 Table 1 (Top Left):

| x | y |
|---|---|
| 5 | 10 |
| 8 | 8 |
|11 | 6 |
|14 | 4 |

Pick first two rows:
Point 1: (5, 10) → x₁=5, y₁=10
Point 2: (8, 8) → x₂=8, y₂=8

Δy = y₂ - y₁ = 8 - 10 = -2
Δx = x₂ - x₁ = 8 - 5 = 3

So, m = Δy / Δx = -2/3

✔ Check with another pair to verify:
Use (8,8) and (11,6):
Δy = 6 - 8 = -2
Δx = 11 - 8 = 3 → still -2/3 ✔️

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🔹 Table 2 (Top Right):

| x | y |
|----|----|
| -2 | 5 |
| 0 | 10 |
| 2 | 15 |
| 4 | 20 |

Pick first two rows:
(-2, 5) and (0, 10)

Δy = 10 - 5 = 5
Δx = 0 - (-2) = 2

m = 5/2

✔ Check with next pair: (0,10) and (2,15)
Δy = 15 - 10 = 5
Δx = 2 - 0 = 2 → still 5/2 ✔️

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🔹 Table 3 (Bottom Left):

| x | y |
|----|----|
| 3 | 20 |
| 6 | 16 |
|12 | 8 |
|15 | 4 |

Pick first two: (3,20) and (6,16)

Δy = 16 - 20 = -4
Δx = 6 - 3 = 3

m = -4/3

✔ Check with (6,16) and (12,8):
Δy = 8 - 16 = -8
Δx = 12 - 6 = 6 → -8/6 = -4/3 ✔️

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🔹 Table 4 (Bottom Right):

| x | -1 | 0 | 1 | 2 |
|----|----|---|---|---|
| y | 0 | 2 | 4 | 6 |

This one is written sideways — but we can read it as:

Points: (-1, 0), (0, 2), (1, 4), (2, 6)

Pick first two: (-1, 0) and (0, 2)

Δy = 2 - 0 = 2
Δx = 0 - (-1) = 1

m = 2/1 = 2

✔ Check with (0,2) and (1,4):
Δy = 4 - 2 = 2
Δx = 1 - 0 = 1 → still 2 ✔️

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## ✔ Final Answers:

Table 1 (top left):
Δy = -2, Δx = 3, m = -2/3

Table 2 (top right):
Δy = 5, Δx = 2, m = 5/2

Table 3 (bottom left):
Δy = -4, Δx = 3, m = -4/3

Table 4 (bottom right):
Δy = 2, Δx = 1, m = 2

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Final Answer:
Table 1: Δy = -2, Δx = 3, m = -2/3
Table 2: Δy = 5, Δx = 2, m = 5/2
Table 3: Δy = -4, Δx = 3, m = -4/3
Table 4: Δy = 2, Δx = 1, m = 2